The Application Of Combination Forecasting In Compositional Data

Compositional data are parts of the whole reflecting the relative information of the data instead of the absolute information. The study of compositional data derived in the study of proportion of mineral composition in the geology. The statistical analysis of compositional data different from that of the other data because of the sum constraint need the transfor-mation of compositional data, because the statistical analysis for the common data always have the hypothesis of normal distribution.Nowadays, it is applied in the management, economics and its importance is highlight in those; field. The technology of combination forecast is widely used in the forecast, which make full use of the single forecast model and make progress on the prediction accuracy. With these merits, combination forecast arouse the concern of many scholars at home and abroad. In this thesis, we applied the transformation of compositional data based on the character of compositional data to make regression forecast and exponential smoothing forecast and finally make combination forecast. The results is illustrated in the tables and figures, from which we find the results of combination forecast is more effective.This thesis is divided into four chapters.The first chapter presents the background of compositional data and the significance of the research and main works. And we introduce the basis theory of compositional data which is produced by Aichison.Chapter two presents the transformations of compositional data which are additive logratio transformation, center logratio transformation, isometric logratio transformation and hyper spherical transformation.In chapter three we present the theory of combination forecast and some forecast stan-dard. Based on the Aichison distance for compositional data, we propose the combinatorial optimization model to figure out the weights. Chapter four presents the illustration of case study. Take examples of the forecasting of three industries in Bei Jing and China, firstly, take transformation of the compositional data; secondly, the forecasting data of transformed data is obtained; thirdly, the predicted compositional data is worked out by the back transformation:and finally we combine the forecasting and get the combination forecast.